# PWMs: Probability weighted moments In TLMoments: Calculate TL-Moments and Convert Them to Distribution Parameters

## Description

Calculates probability weighted moments up to a specific order. Note that PWMs start with order 0. Acceptable input types are numeric vectors, matrices, lists, and data.frames.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```PWMs(x, ...) ## S3 method for class 'numeric' PWMs(x, max.order = 4L, na.rm = FALSE, ...) ## S3 method for class 'matrix' PWMs(x, max.order = 4L, na.rm = FALSE, ...) ## S3 method for class 'list' PWMs(x, max.order = 4L, na.rm = FALSE, ...) ## S3 method for class 'data.frame' PWMs(x, formula, max.order = 4L, na.rm = FALSE, ...) ## S3 method for class 'TLMoments' PWMs(x, ...) ```

## Arguments

 `x` numeric vector or matrix, list, or data.frame of data OR an object of TLMoments. `...` additional arguments. `max.order` integer, maximal order of PWMs. `na.rm` logical, indicates if NAs should be removed. `formula` if x is of type data.frame a formula has to be submitted.

## Value

numeric vector, matrix, list, or data.frame consisting of the PWMs and with class `PWMs`. The object contains the following attributes:

• `order`: a integer vector with corresponding PWM orders

• `source`: a list with background information (used function, data, n, formula; mainly for internal purposes)

The attributes are hidden in the print-function for a clearer presentation.

## References

Greenwood, J. A., Landwehr, J. M., Matalas, N. C., & Wallis, J. R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15(5), 1049-1054.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34``` ```# Generating data sets: xmat <- matrix(rnorm(100), nc = 4) xvec <- xmat[, 3] xlist <- lapply(1L:ncol(xmat), function(i) xmat[, i]) xdat <- data.frame( station = rep(letters[1:2], each = 50), season = rep(c("S", "W"), 50), hq = as.vector(xmat) ) # Calculating PWMs from data: PWMs(xvec) PWMs(xmat) PWMs(xlist) PWMs(xdat, formula = hq ~ station) PWMs(xdat, formula = hq ~ season) PWMs(xdat, formula = hq ~ .) PWMs(xdat, formula = . ~ station + season) # Calculating PWMs from L-moments: PWMs(TLMoments(xvec)) PWMs(TLMoments(xmat)) PWMs(TLMoments(xlist)) PWMs(TLMoments(xdat, hq ~ station)) PWMs(TLMoments(xdat, hq ~ season)) PWMs(TLMoments(xdat, hq ~ .)) PWMs(TLMoments(xdat, . ~ station + season)) # In data.frame-mode invalid names are preceded by "." xdat <- data.frame( beta0 = rep(letters[1:2], each = 50), beta1 = as.vector(xmat) ) PWMs(xdat, formula = beta1 ~ beta0) ```

TLMoments documentation built on Dec. 4, 2019, 5:06 p.m.